Formula for the Volume of a Cylinder

A cylinder is a three-dimensional shape that is formed by two congruent circles connected by parallel lines. The volume of a cylinder is the amount of space inside the cylinder. Because the formula is for a three-dimensional object's volume, the resulting measurement will be in units cubed, such as cubic meters or cubic feet. Examples of cylinders include pipes and batons.

  1. Formula

    • The formula for the volume of a cylinder is πr^2h, where r is the radius of the base and h is the height of the cylinder. The radius is calculated by measuring how wide the base is from one point on the circle straight through the center of the circle to the other side and dividing that distance by 2. The height is measured as the distance between the two circles. Since all lines between the two circles are parallel, it does not matter where along the surface you measure the distance. For example, if the distance across, also known as the "diameter," is 10 meters, the radius would be 5 meters. If the height is 6 meters, the volume would be 471 cubic meters.

    Reasoning for the Formula

    • Since the formula is determining the space inside a three-dimensional object, there must be three dimensions that are involved in the calculation. For example, a rectangular prism uses length, width and height. Since the cylinder does not have a constant width and length, you must use the area of the circle to represent the two dimensions of width and length. The third dimension is height.

    Applications for the Formula

    • The volume of a cylinder is applicable to many situations in real life. For example, when a plumber is planning a system of pipes, she must calculate the amount of water flow that will be needed to make sure the pipes don't back up. The plumber will estimate what the maximum amount of water any given section of pipe will have to hold and then use the formula for the volume of a cylinder to find out what the dimensions of the pipe have to be. Also, a town planning a cylindrical water tower will know how much water it plans to store and can then calculate the dimensions of the water tower accordingly.

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